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2 years ago

Emilio is pickling tomatillos with his grandfather. The tomatillos are approximately

Mathematics

1 answer:

Fudgin [204]2 years ago

8 0

The jar can hold a total of three tomatoes at a time.

<h3>What is volume?</h3>

Volume is the amount of space occupied by a three dimensional shape or object.

The tomatoes is spherical with a diameter of 6 cm (radius = 6/2 = 3cm), hence:

Volume of tomatoes = (4/3) * π * radius³ = (4/3) * π * 4³ = 268 cm³

The jar is cylinder with diameter of 8 cm (radius = 8/2 = 4) and a height of 21 cm, hence:

Volume of jar = π * radius² * height = π * 4² * 21 = 1055.6 cm³

Amount of tomatoes that can be contained in jar = 1055.6 cm³ / 268 cm³ = 3.9

The jar can hold a total of three tomatoes at a time.

Find out more on volume at: brainly.com/question/12410983

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3 years ago

a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his p

ZanzabumX [31]

Complete Question:

A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.

a. What is his maximum profit per day?

b. How many cans must be sold in order to obtain the maximum profit?

Answer:

a. $450

b. 1500 cans

Step-by-step explanation:

Given the following quadratic function;

P(x) = -0.001x² + 3x - 1800 ......equation 1

a. To find his maximum profit per day;

Since P(x) is a quadratic equation, P(x) would be maximum when $x = \frac {-b}{2a}$

Note : the standard form of a quadratic equation is ax² + bx + c = 0 ......equation 2

Comparing eqn 1 and eqn 2, we have;

a = -0.001, b = 3 and c = -1800

Now, we determine the maximum profit;

$x = \frac {-b}{2a}$

Substituting the values, we have;

$x = \frac {-3}{2*(-0.001)}$

Cancelling out the negative signs, we have;

$x = \frac {3}{2*0.001}$

$x = \frac {3}{0.002}$

x at maximum = 1500

Substituting the value of "x" into equation 1;

P(1500) = -0.001 * 1500² + 3(1500) - 1800

P(1500) = -0.001 * 2250000 + 4500 - 1800

P(1500) = -2250 + 2700

P(1500) = $450

b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.

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